SOLUTION: In a change purse there are some nickels some dimes and some quarters. There are 100 coins altogether and the number of nickels are the same as the number of dimes and quarters com

Question 177294: In a change purse there are some nickels some dimes and some quarters. There are 100 coins altogether and the number of nickels are the same as the number of dimes and quarters combined. the total value of thecoins is $12.30. how many of each coin do i have?

> it can be answered by any means
> i got n=nickels
d=dimes
q=quarters
> n+d+q=100
> n=d+q
> .5n +.10d +.25q =$12.30
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
n + d + q = 100
.05*n + .1*d + .25*q = 12.30
n = d + q
so far so good.
substituting in the first equation, we get:
d + q + d + q = 100
combining like terms:
2d + 2q = 100
dividing both sides by 2:
d + q = 50
d = 50 - q
since n = d + q
and d = 50 - q
then n = 50 - q + q = 50
we have:
n = 50
d = 50 - q
substituting in second equation of:
.05*n + .1*d + .25*q = 12.30
we get:
.05*50 + .1*(50-q) + .25*q = 12.3
simplifying we get:
2.5 + 5 - .1*q + .25*q = 12.3
combining like terms we get:
7.5 + .15*q = 12.3
subtracting 7.5 from both sides we get:
.15*q = 12.3 - 7.5 = 4.8
dividing both sides by .15 we get:
q = 4.8/.15 = 32
since d = 50 - q, this means that d = 50 - 32 = 18
we have:
n = 50
d = 18
q = 32
n + q + d = 50 + 18 + 32 = 100
.05*n + .1*d + .25*q = .05*50 + .1*18 + .25*32 = 2.5 + 1.8 + 8 = 12.3
both equations are satisfied, so the number of each coins is:
50 nickels
18 dimes
32 quarters

RELATED QUESTIONS
in your pocket you have some nickels, dimes, and quarters. there are 20 coins altogether... (answered by richwmiller)

There are 52 coins in a purse. Some of them are quarters, and some are dimes. The... (answered by stanbon,algebrahouse.com)

A purse contains 26 coins, some of which are dimes and the rest nickels. Altogether, the... (answered by CubeyThePenguin,ikleyn)

a change purse contains only quarters and dimes. There are 15 coins in the purse. the... (answered by Edwin McCravy)

In a bowl there are some nickels, dimes and quarters. There are 5 nickels for every 6... (answered by greenestamps)

The amount of money in cents in a jar containing n nickels and some dimes and some... (answered by mananth)

"A purse contains 22 coins, some of wich are dimes and the rest, quarters, Altogether,... (answered by checkley71)

In a bag, there are some nickels and dimes. If there are 79 coins together and the total... (answered by greenestamps)

Janice has 16 coins in her purse. Some of the coins are dimes, some are quarters. The... (answered by stanbon)